Donkey pronoun
Encyclopedia
A donkey pronoun is a pronoun that is bound
Bound variable pronoun
A bound variable pronoun is one which has a quantified determiner phrase as its antecedent.- Bibliography :* Hendrick, Randall . "", pages 103–115 in Heinz & Ntelitheos UCLA Working Papers in Linguistics 12 [Proceedings of AFLA XII].* . "". Pages 125–240 in Gert Webelhuth . : principles and...

 in semantics
Semantics
Semantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....

 but not syntax
Syntax
In linguistics, syntax is the study of the principles and rules for constructing phrases and sentences in natural languages....

.
Some writers prefer the term donkey anaphora, since it is the referential
Reference
Reference is derived from Middle English referren, from Middle French rèférer, from Latin referre, "to carry back", formed from the prefix re- and ferre, "to bear"...

 aspects and discourse
Discourse
Discourse generally refers to "written or spoken communication". The following are three more specific definitions:...

 or syntactic
Syntax
In linguistics, syntax is the study of the principles and rules for constructing phrases and sentences in natural languages....

 context that are of interest to researchers (see anaphora
Anaphora (linguistics)
In linguistics, anaphora is an instance of an expression referring to another. Usually, an anaphoric expression is represented by a pro-form or some other kind of deictic--for instance, a pronoun referring to its antecedent...

). The terms d-type or e-type pronoun are also used, mutually exclusively, dependent on theoretical approach to interpretation
Interpretation (logic)
An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation...

. A sentence containing a donkey pronoun is sometimes called a donkey sentence
Donkey sentence
Donkey sentences are sentences that contain a certain type of anaphora, such as:* Every farmer who owns a donkey beats it.* Every police officer who arrested a murderer insulted him....

.

The term donkey pronoun was coined from a counterexample
Counterexample
In logic, and especially in its applications to mathematics and philosophy, a counterexample is an exception to a proposed general rule. For example, consider the proposition "all students are lazy"....

 provided by Peter Geach
Peter Geach
Peter Thomas Geach is a British philosopher. His areas of interest are the history of philosophy, philosophical logic, and the theory of identity.He was educated at Balliol College, Oxford...

 (1962) to Richard Montague
Richard Montague
Richard Merett Montague was an American mathematician and philosopher.-Career:At the University of California, Berkeley, Montague earned an B.A. in Philosophy in 1950, an M.A. in Mathematics in 1953, and a Ph.D. in Philosophy 1957, the latter under the direction of the mathematician and logician...

's proposal for a generalized formal representation of quantification
Quantification
Quantification has several distinct senses. In mathematics and empirical science, it is the act of counting and measuring that maps human sense observations and experiences into members of some set of numbers. Quantification in this sense is fundamental to the scientific method.In logic,...

 in natural language
Natural language
In the philosophy of language, a natural language is any language which arises in an unpremeditated fashion as the result of the innate facility for language possessed by the human intellect. A natural language is typically used for communication, and may be spoken, signed, or written...

. The example was reused by David Lewis
David Kellogg Lewis
David Kellogg Lewis was an American philosopher. Lewis taught briefly at UCLA and then at Princeton from 1970 until his death. He is also closely associated with Australia, whose philosophical community he visited almost annually for more than thirty years...

 (1975), Gareth Evans
Gareth Evans (philosopher)
Gareth Evans was a British philosopher.-Life:Gareth Evans studied Philosophy, Politics and Economics at University College, Oxford . His philosophy tutor was Peter Strawson...

 (1977) and many others, and is still quoted in recent publications. The original donkey sentence is as follows.
  • Every farmer who owns a donkey beats it. — Peter Geach
    Peter Geach
    Peter Thomas Geach is a British philosopher. His areas of interest are the history of philosophy, philosophical logic, and the theory of identity.He was educated at Balliol College, Oxford...

    , Reference and Generality

This sentence is significant because it represents a class of well-formed natural language sentences that defy straightforward attempts to generate their formal language
Formal language
A formal language is a set of words—that is, finite strings of letters, symbols, or tokens that are defined in the language. The set from which these letters are taken is the alphabet over which the language is defined. A formal language is often defined by means of a formal grammar...

 equivalents. The difficulty is with understanding how English speakers parse
Parsing
In computer science and linguistics, parsing, or, more formally, syntactic analysis, is the process of analyzing a text, made of a sequence of tokens , to determine its grammatical structure with respect to a given formal grammar...

 the scope of quantification in such sentences.
Additionally, the indefinite article 'a' is normally understood as an existential quantifier, but the most natural reading of the donkey sentence requires it to be understood as a nested universal quantifier. There are other features of the sentence that require careful consideration for adequate description. (Notice, however, how reading "each" in place of "every" simplifies the formal analysis.)

The donkey pronoun in the example sentence is the word it.

There is nothing "wrong" with donkey sentences. They are grammatically "correct", they are well-formed, their syntax is regular. They are also logically meaningful, they have well-defined truth conditions, their semantics are unambiguous. It is precisely this that makes them interesting. The difficulty is with explaining how syntactic elements give rise to the semantic result and in a way that generalizes consistently with all other language use. Then, for example, we could program a computer to accurately translate natural language forms into logical form
Logical form
In logic, the logical form of a sentence or set of sentences is the form obtained by abstracting from the subject matter of its content terms or by regarding the content terms as mere placeholders or blanks on a form...

. The question is, how are natural language users, apparently effortlessly, agreeing on the meaning of sentences like these?

There may be several equivalent ways of describing this process. In fact, Hans Kamp
Hans Kamp
Johan Anthony Willem Kamp is a Dutch philosopher and linguist, responsible for introducing Discourse Representation Theory in 1981. Kamp received a Ph.D. in Philosophy from UCLA in 1968...

 (1981) and Irene Heim
Irene Heim
Irene Roswitha Heim is a linguist and noted specialist in semantics. She was a professor at the University of Texas at Austin and UCLA before finally moving to the Massachusetts Institute of Technology in 1989, where she is Professor of Linguistics and Head of the Linguistics Section of the...

 (1982) independently proposed very similar accounts in different terminology, which they called discourse representation theory
Discourse representation theory
Discourse Representation Theory is a framework for exploring meaning under a formal semantics approach. One of the main differences between DRT-style approaches and traditional Montagovian approaches is that DRT-style approaches include a level of abstract mental representations within its...

 (DRT) and file change semantics (FCS) respectively.

In 2007, Adrian Brasoveanu published studies of donkey pronoun analogs in Hindi
Hindi
Standard Hindi, or more precisely Modern Standard Hindi, also known as Manak Hindi , High Hindi, Nagari Hindi, and Literary Hindi, is a standardized and sanskritized register of the Hindustani language derived from the Khariboli dialect of Delhi...

, and analysis of complex and modal
Modal logic
Modal logic is a type of formal logic that extends classical propositional and predicate logic to include operators expressing modality. Modals — words that express modalities — qualify a statement. For example, the statement "John is happy" might be qualified by saying that John is...

 versions of donkey pronouns in English.

Discourse Representation Theory

Donkey sentences became a major force in advancing semantic
Semantics
Semantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....

 research in the 1980s, with the introduction of discourse representation theory
Discourse representation theory
Discourse Representation Theory is a framework for exploring meaning under a formal semantics approach. One of the main differences between DRT-style approaches and traditional Montagovian approaches is that DRT-style approaches include a level of abstract mental representations within its...

 (DRT). During that time, an effort was made to settle the inconsistencies which arose from the attempts to translate donkey sentences into first-order logic
First-order logic
First-order logic is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic...

.

Donkey sentences present the following problem, when represented in first-order logic: The systematic translation of every existential expression in the sentence into existential quantifiers produces an incorrect representation of the sentence, since it leaves a free occurrence of the variable y in BEAT(x.y):


Trying to extend the scope of the existential quantifier also does not solve the problem:


In this case, the logical translation fails to give correct truth conditions to donkey sentences: Imagine a situation where there is a farmer owning a donkey and a pig, and not beating any of them. The formula will be true in that situation, because for each farmer we need to find at least one object that either is not a donkey owned by this farmer, or is beaten by the farmer. Hence, if this object denotes the pig, the sentence will be true in that situation.

A correct translation into first-order logic for the donkey sentence seems to be:


Unfortunately, this translation leads to a serious problem of inconsistency. Indefinites must sometimes be interpreted as existential quantifiers, and other times as universal quantifiers, without any apparent regularity.

The solution that DRT
Discourse representation theory
Discourse Representation Theory is a framework for exploring meaning under a formal semantics approach. One of the main differences between DRT-style approaches and traditional Montagovian approaches is that DRT-style approaches include a level of abstract mental representations within its...

 provides for the donkey sentence problem can be roughly outlined as follows: The common semantic function of non-anaphoric noun phrase
Noun phrase
In grammar, a noun phrase, nominal phrase, or nominal group is a phrase based on a noun, pronoun, or other noun-like word optionally accompanied by modifiers such as adjectives....

s is the introduction of a new discourse referent, which is in turn available for the binding of anaphoric expressions. No quantifiers are introduced into the representation, thus overcoming the scope problem that the logical translations had.

See also

  • Epsilon calculus
    Epsilon calculus
    Hilbert's epsilon calculus is an extension of a formal language by the epsilon operator, where the epsilon operator substitutes for quantifiers in that language as a method leading to a proof of consistency for the extended formal language...

  • Generic antecedent
    Generic antecedent
    Generic antecedents are representatives of classes, referred to in ordinary language by another word , in a situation in which gender is typically unknown or irrelevant. These mostly arise in generalizations and are particularly common in abstract, theoretical or strategic discourse...

  • Lambda calculus
    Lambda calculus
    In mathematical logic and computer science, lambda calculus, also written as λ-calculus, is a formal system for function definition, function application and recursion. The portion of lambda calculus relevant to computation is now called the untyped lambda calculus...

  • Montague grammar
    Montague grammar
    Montague grammar is an approach to natural language semantics, named after American logician Richard Montague. The Montague grammar is based on formal logic, especially higher order predicate logic and lambda calculus, and makes use of the notions of intensional logic, via Kripke models...

  • Singular they
    Singular they
    Singular they is the use of they to refer to an entity that is not plural, or not necessarily plural. Though singular they is widespread in everyday English and has a long history of usage, debate continues about its acceptability...

  • Donkey sentence
    Donkey sentence
    Donkey sentences are sentences that contain a certain type of anaphora, such as:* Every farmer who owns a donkey beats it.* Every police officer who arrested a murderer insulted him....


External links

  • The Handbook of Philosophical Logic
  • Discourse Representation Theory
  • Introduction to Discourse Representation Theory
  • SEP Entry
  • Archive of CSI 5386 Donkey Sentence Discussion
  • Barker, Chris. 'A Presuppositional Account of Proportional Ambiguity'. In Proceedings of Semantic and Linguistic Theory (SALT) 3. Ithaca, New York: Cornell University
    Cornell University
    Cornell University is an Ivy League university located in Ithaca, New York, United States. It is a private land-grant university, receiving annual funding from the State of New York for certain educational missions...

    , 1993. Pages 1–18.
  • Brasoveanu, Adrian. 'Donkey Pluralities: Plural Information States vs. Non-Atomic Individuals'. In Proceedings of Sinn und Bedeutung 11. Edited by E. Puig-Waldmüller. Barcelona: Pompeu Fabra University
    Pompeu Fabra University
    Pompeu Fabra University is a university in Barcelona, Catalonia, Spain. It is widely considered to be one of the best universities in Spain and in Europe, and was ranked 1st in scientific productivity in Spain in 2009. Founded in 1990, it is named after the Catalan philologist Pompeu Fabra...

    , 2007. Pages 106–120.
  • Evans, Gareth
    Gareth Evans (philosopher)
    Gareth Evans was a British philosopher.-Life:Gareth Evans studied Philosophy, Politics and Economics at University College, Oxford . His philosophy tutor was Peter Strawson...

    . 'Pronouns, Quantifiers, and Relative Clauses (I)'. Canadian Journal of Philosophy 7 (1977): 467–536.
  • Geurts, Bart. 'Donkey Business'. Linguistics and Philosophy 25 (2002): 129–156.
  • Huang, C-T James. 'Logical Form'. Chapter 3 in Government and Binding Theory and the Minimalist Program: Principles and Parameters in Syntactic Theory edited by Gert Webelhuth. Oxford and Cambridge: Blackwell Publishing
    Blackwell Publishing
    Wiley-Blackwell is the international scientific, technical, medical, and scholarly publishing business of John Wiley & Sons. It was formed by the merger of John Wiley's Global Scientific, Technical, and Medical business with Blackwell Publishing, after Wiley took over Blackwell Publishing in...

    , 1995. Pages 127–177.
  • Kamp, Hans
    Hans Kamp
    Johan Anthony Willem Kamp is a Dutch philosopher and linguist, responsible for introducing Discourse Representation Theory in 1981. Kamp received a Ph.D. in Philosophy from UCLA in 1968...

    . 'A Theory of Truth and Semantic Representation'. In J. Groenendijk and others (eds.). Formal Methods in the Study of Language. Amsterdam: Mathematics Center, 1981.
  • Kitagawa, Yoshihishi. 'Copying Variables'. Chapter 2 in Functional Structure(s), Form and Interpretation: Perspectives from East Asian Languages. Edited by Yen-hui Audrey Li and others. Routledge
    Routledge
    Routledge is a British publishing house which has operated under a succession of company names and latterly as an academic imprint. Its origins may be traced back to the 19th-century London bookseller George Routledge...

    , 2003. Pages 28–64.
  • Lewis, David
    David Kellogg Lewis
    David Kellogg Lewis was an American philosopher. Lewis taught briefly at UCLA and then at Princeton from 1970 until his death. He is also closely associated with Australia, whose philosophical community he visited almost annually for more than thirty years...

    . 'Adverbs of Quantification'. In Formal Semantics of Natural Language. Edited by Edward L Keenan. Cambridge: Cambridge University Press
    Cambridge University Press
    Cambridge University Press is the publishing business of the University of Cambridge. Granted letters patent by Henry VIII in 1534, it is the world's oldest publishing house, and the second largest university press in the world...

    , 1975. Pages 3–15.
  • Montague, Richard
    Richard Montague
    Richard Merett Montague was an American mathematician and philosopher.-Career:At the University of California, Berkeley, Montague earned an B.A. in Philosophy in 1950, an M.A. in Mathematics in 1953, and a Ph.D. in Philosophy 1957, the latter under the direction of the mathematician and logician...

    . 'The Proper Treatment of Quantification in Ordinary English'. In KJJ Hintikka and others (eds). Proceedings of the 1970 Stanford Workshop on Grammar and Semantics. Dordrecht: Reidel, 1973. Pages 212–242.

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    Natural Language Semantics: An International Journal of Semantics and Its Interfaces in Grammar is a leading international peer-reviewed semantics journal published by Springer Netherlands . It is devoted to semantics and its interfaces in grammar, especially in syntax...

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    Linguistic Inquiry is a peer-reviewed academic journal in generative linguistics published by the MIT Press since 1970. Ever since its foundation, it has been edited by Samuel Jay Keyser. Many seminal linguistic articles first appeared on its pages. The volumes since 1998 are available online via...

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  • Barker, Chris. 'Presuppositions for Proportional Quantifiers'. Natural Language Semantics
    Natural Language Semantics
    Natural Language Semantics: An International Journal of Semantics and Its Interfaces in Grammar is a leading international peer-reviewed semantics journal published by Springer Netherlands . It is devoted to semantics and its interfaces in grammar, especially in syntax...

     4 (1996): 237–259.
  • Brasoveanu, Adrian. Structured Nominal and Modal Reference. Rutgers University
    Rutgers University
    Rutgers, The State University of New Jersey , is the largest institution for higher education in New Jersey, United States. It was originally chartered as Queen's College in 1766. It is the eighth-oldest college in the United States and one of the nine Colonial colleges founded before the American...

     PhD dissertation, 2007.
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    Natural Language Semantics: An International Journal of Semantics and Its Interfaces in Grammar is a leading international peer-reviewed semantics journal published by Springer Netherlands . It is devoted to semantics and its interfaces in grammar, especially in syntax...

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    The University of Massachusetts Amherst is a public research and land-grant university in Amherst, Massachusetts, United States and the flagship of the University of Massachusetts system...

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    Gareth Evans was a British philosopher.-Life:Gareth Evans studied Philosophy, Politics and Economics at University College, Oxford . His philosophy tutor was Peter Strawson...

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    Linguistic Inquiry is a peer-reviewed academic journal in generative linguistics published by the MIT Press since 1970. Ever since its foundation, it has been edited by Samuel Jay Keyser. Many seminal linguistic articles first appeared on its pages. The volumes since 1998 are available online via...

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    Peter Geach
    Peter Thomas Geach is a British philosopher. His areas of interest are the history of philosophy, philosophical logic, and the theory of identity.He was educated at Balliol College, Oxford...

    . Reference and Generality: An Examination of Some Medieval and Modern Theories. Ithaca, New York: Cornell University Press
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    The Cornell University Press, established in 1869 but inactive from 1884 to 1930, was the first university publishing enterprise in the United States.A division of Cornell University, it is housed in Sage House, the former residence of Henry William Sage....

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    Elsevier is a publishing company which publishes medical and scientific literature. It is a part of the Reed Elsevier group. Based in Amsterdam, the company has operations in the United Kingdom, USA and elsewhere....

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    Language is a peer-reviewed quarterly academic journal published by the Linguistic Society of America since 1925. It covers all aspects of linguistics, focusing on the area of theoretical linguistics...

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    Irene Roswitha Heim is a linguist and noted specialist in semantics. She was a professor at the University of Texas at Austin and UCLA before finally moving to the Massachusetts Institute of Technology in 1989, where she is Professor of Linguistics and Head of the Linguistics Section of the...

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    Irene Roswitha Heim is a linguist and noted specialist in semantics. She was a professor at the University of Texas at Austin and UCLA before finally moving to the Massachusetts Institute of Technology in 1989, where she is Professor of Linguistics and Head of the Linguistics Section of the...

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    The University of Massachusetts Amherst is a public research and land-grant university in Amherst, Massachusetts, United States and the flagship of the University of Massachusetts system...

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    Cognitive psychology is a subdiscipline of psychology exploring internal mental processes.It is the study of how people perceive, remember, think, speak, and solve problems.Cognitive psychology differs from previous psychological approaches in two key ways....

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    Cornell University is an Ivy League university located in Ithaca, New York, United States. It is a private land-grant university, receiving annual funding from the State of New York for certain educational missions...

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    Theoretical Linguistics is an international peer-reviewed journal of theoretical linguistics published by Mouton de Gruyter. Since 2001 Prof. Manfred Krifka has been its editor. Each issue contains one long target article, together with several shorter reactions, comments and reflections on it...

     15 (1989): 263–286.
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    David Kellogg Lewis was an American philosopher. Lewis taught briefly at UCLA and then at Princeton from 1970 until his death. He is also closely associated with Australia, whose philosophical community he visited almost annually for more than thirty years...

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    Wiley-Blackwell is the international scientific, technical, medical, and scholarly publishing business of John Wiley & Sons. It was formed by the merger of John Wiley's Global Scientific, Technical, and Medical business with Blackwell Publishing, after Wiley took over Blackwell Publishing in...

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    Stephen Roy Albert Neale is Distinguished Professor of Philosophy and Linguistics and holder of the John H. Kornblith Family Chair in the Philosophy of Science and Values at the Graduate Center, City University of New York...

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    The MIT Press is a university press affiliated with the Massachusetts Institute of Technology in Cambridge, Massachusetts .-History:...

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    Stephen Roy Albert Neale is Distinguished Professor of Philosophy and Linguistics and holder of the John H. Kornblith Family Chair in the Philosophy of Science and Values at the Graduate Center, City University of New York...

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    The Journal of Philosophy is a monthly peer-reviewed academic journal on philosophy. Its stated purpose is "To publish philosophical articles of current interest and encourage the interchange of ideas, especially the exploration of the borderline between philosophy and other disciplines." The...

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    Willard Van Orman Quine
    Willard Van Orman Quine was an American philosopher and logician in the analytic tradition...

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    Word and Object
    Word and Object is a 1960 book of epistemology by Willard Van Orman Quine. In it, Quine develops his thesis of the Indeterminacy of translation....

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    The MIT Press is a university press affiliated with the Massachusetts Institute of Technology in Cambridge, Massachusetts .-History:...

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    The Journal of Semantics is a leading international peer-reviewed journal of semantics of natural languages published by Oxford University Press. Its current editor is Philippe Schlenker . The journal is available online with subscription via OxfordJournals....

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    The University of Texas at Austin is a state research university located in Austin, Texas, USA, and is the flagship institution of the The University of Texas System. Founded in 1883, its campus is located approximately from the Texas State Capitol in Austin...

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